How do you take the derivative of #tan^3 (3x-1)#?

1 Answer
Apr 30, 2018

#9tan^2(3x-1)sec^2(3x-1)#

Explanation:

#"differentiate using the "color(blue)"chain rule"#

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#"here "y=tan^3(3x-1)=(tan(3x-1))^3#

#rArrdy/dx=3(tan(3x-1))^2xxd/dx(tan(3x-1))#

#color(white)(rArrdy/dx)=3tan^2(3x-1)xxsec^2(3x-1)xxd/dx(3x-1)#

#color(white)(rArrdy/dx)=9tan^2(3x-1)sec^2(3x-1)#